1. **Problem:** Point P(-9, 4) lies on the terminal arm of an angle on the Cartesian plane. a) Find the measure of the related acute angle to the nearest degree. b) Find the principal angle of the terminal arm. 2. **Formula and rules:** - The related acute angle is the smallest angle between the terminal arm and the x-axis. - The principal angle is the angle between 0° and 360° that corresponds to the terminal arm. - Use the tangent function: $$\tan(\theta) = \frac{y}{x}$$ where $(x,y)$ are coordinates of point P. 3. **Step a: Calculate the related acute angle** - Given $P(-9,4)$, calculate $$\tan(\theta) = \left|\frac{4}{-9}\right| = \frac{4}{9}$$ - Find $$\theta = \arctan\left(\frac{4}{9}\right)$$ - Using a calculator, $$\theta \approx 23.96^\circ$$ - The related acute angle is approximately $24^\circ$. 4. **Step b: Calculate the principal angle** - Since $x < 0$ and $y > 0$, point P is in Quadrant II. - Principal angle $$= 180^\circ - \theta = 180^\circ - 23.96^\circ = 156.04^\circ$$ - Rounded, the principal angle is $156^\circ$. **Final answers:** - Related acute angle: $24^\circ$ - Principal angle: $156^\circ$